Mathematical Theory and Application

The heart of any controls system is the math that goes into it. While we can do without the math for many simple machines, as soon as we want to do anything interesting it's time to break out the calculators.

Controls has many levels of math. First, you must have an understanding of your system and dynamics. Since controls and automation are all about trying to predict and react to a current state, there's not much you can do if you don't have the first clue about what you're trying to control.

Secondly, controls math involves many different schemes for making a controller. Some control schemes are obvious, such as the fastest way for a rocket to go from Sol to Alpha Centauri (accelerate at maximum thrust until the midway point, then turn around and decelerate at maximum thrust until arrival), but most are not. Moreover, there is usually no "perfect" answer. More often than not, you have to finagle the control variables in simulation (if your model is good enough) or in empiric tests. It's an engineering compromise. You want the model to go as fast as possible (cool) but not so fast that the model physically self-destructs (uncool).